Banach空间上的囿变算子及算子幂级数收敛定理

OPerator of Bounded Variation and the Convergence Theorems of Operator-Power Series on Banach SPace

在Banach空间中如何构造或定义抽象的幂级数模式,以及如何建立Banach空间中幂级数的理论,这一问题在Banach空间理论中似不多见。 本文拟给出赋范线性空间上的囿变算子及一致囿变算子的概念,根据中关于算子幂级数的有关定义,进而在Banach空间得出算子幂级数收敛或一致收敛的一系列定理。

How is the power series in Banach analysis constructed? and how is the theory of the power series on Banach space set up? These have been uncovered new land in rnodern analysis. In this paper we give the concepts of operator of (uniform) bounded variation and provide some(uniform) convergence theorems about operator power series on Banach space.